SOLUTION: find the following for the function f(x)=(x+4)^2(x-2)^2 a. find the x and y intercepts b.determine whether the graph of f crosses or touches the x-axis at each untercept c.put a

Question 865756: find the following for the function f(x)=(x+4)^2(x-2)^2
a. find the x and y intercepts
b.determine whether the graph of f crosses or touches the x-axis at each untercept
c.put all the information together to obtain graph of f
thanks in advance for the help

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

This is already in factored form. x intercepts are -4 and +2.
y-intercept happens for .

Examine the function factors very carefully. Each individual binomial factor may be less than, equal to, or greater than zero; but because both factors are squared, f(x) stays POSITIVE, so will always be at or above the horizontal axis. This means, f(x) NEVER crosses the x axis at any x intercept.

The vertical labeling is imprecise, but here is a fair representation of the graph:

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